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Minimising computational complexity of the RRT algorithm a practical approach
Abstract and Figures
Sampling based techniques for robot motion plan- ning have become more widespread during the last decade. The algorithms however, still struggle with for example narrow passages in the configuration space and suffer from high number of necessary samples, especially in higher dimensions. A widely used method is Rapidly-exploring Random Trees (RRT's). One problem with this method is the nearest neighbour search time, which grows significantly when adding a large number of vertices. We propose an algorithm which decreases the computation time, such that more vertices can be added in the same amount of time to generate better trajectories. The algorithm is based on subdividing the configuration space into boxes, where only specific boxes needs to be searched to find the nearest neighbour. It is shown that the computational complexity is lowered from a theoretical point of view. The result is an algorithm that can provide better trajectories within a given time period, or alternatively compute trajectories faster. In simulation the algorithm is verified for a simple RRT implementation and in a more specific case where a robot has to plan a path through a human inhabited environment. I. INTRODUCTION
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... In reality, the environment is not always known in advance, so the algorithm is not always effective. For a single query problem, the RRT is probabilistically complete and faster than the PRM 15 . However, the RRT algorithms' path is a non-optimal solution, which is its primary limitation. ...
Autonomous Mobile Robots' performance relies on intelligent motion planning algorithms. In autonomous mobile robots, sampling-based path-planning algorithms are widely used. One of the efficient sampling-based path planning algorithms is the Rapidly Exploring Random Tree (RRT). However, the solution provided by RRT is suboptimal. An RRT extension known as RRT* is optimal, but it takes time to converge. To improve the RRT* slow convergence problem, a goal-oriented sampling-based RRT* algorithm known as GS-RRT* is proposed in this paper. The focus of the proposed research work is to reduce unwanted sample exploration and solve the slow convergence problem of RRT* by taking more samples in the vicinity of the goal region. The proposed research work is validated in three different environments with a map size of 384*384 and compared to the existing algorithms: RRT, Goal-directed RRT(G-RRT), RRT*, and Informed-RRT*. The proposed research work is compared with existing algorithms using four metrics: path length, time to find the solution, the number of nodes visited, and the convergence rate. The validation is done in the Gazebo Simulation and on a TurtleBot3 mobile robot using the Robotics Operating System (ROS). The numerical findings show that the proposed research work improves the convergence rate by an average of 33% over RRT* and 27% over Informed RRT*, and the node exploration is 26% better than RRT* and 20% better than Informed RRT*.
... In the simplest case, the path is a straight line connecting from the start to the goal in the latent space, and I 1 is obtained by dividing the straight line distance L 1 in latent space by the distance D 1 per step, O(I 1 = L 1 /D 1 ). The computational complexity of the RRT is O(I 2 2 ) for the number of iterations I 2 [32,33]. Assume that the number of iterations I 2 is sufficiently large so that the robot's degrees of freedom can be ignored. ...
We propose a new method for collision-free planning using Conditional Generative Adversarial Networks (cGANs) to transform between the robot's joint space and a latent space that captures only collision-free areas of the joint space, conditioned by an obstacle map. Generating multiple plausible trajectories is convenient in applications such as the manipulation of a robot arm by enabling the selection of trajectories that avoids collision with the robot or surrounding environment. In the proposed method, various trajectories that avoid obstacles can be generated by connecting the start and goal state with arbitrary line segments in this generated latent space. Our method provides this collision-free latent space, after which any planner, using any optimization conditions, can be used to generate the most suitable paths on the fly. We successfully verified this method with a simulated and actual UR5e 6-DoF robotic arm. We confirmed that different trajectories could be generated depending on optimization conditions.
... It can rapidly acquire the global trajectory in an extensive range of interest workspace (Fig. 8). If we proceed N iterations, the complexity is O(N 2 − N ) [17]. It is obvious that the HAT-based IPP with RRT* approach generates the global trajectory in the large space in a relatively short period. ...
... The sampling points of the traditional RRT algorithm are highly random, and the generated paths often have numerous redundant nodes [37]. The efficiency in complex environments with many obstacles is low, making path pruning an essential step. ...
Hazardous weather has become a major cause of flight delays in recent years. With the development of satellite navigation systems, the study of flight-path optimization under hazardous weather conditions has become especially important. In this study, radar data were used as the basis for the initial flight-restricted area under hazardous weather conditions, and the Graham algorithm was used to delineate the dynamic flight-restricted area by comprehensively considering the hazardous weather boundary changes along with the speed and direction. Then, under the grid environment model, the range of influence, size, and distribution characteristics of the flight-restricted area was examined, and the path optimization model was created according to constraints related to the path distance, corner size, and number of turning points. An improved F-RRT ∗ algorithm was developed to solve the model. The algorithm can overcome the problems of traditional path planning algorithms, such as strong randomness, poor guidance, slow convergence speed, unsmooth paths, and poor tracing smoothness. Finally, a simulation analysis was conducted on the Guiyang–Guangzhou route in China as an example. This study can address the drawbacks of existing research on route change and provide sufficient theoretical support and reference for the implementation of specific route change plans in the future.
... It constructs a tree incrementally from the starting point to the goal in a given configuration space. Even though the RRT is faster than the PRM [9] for single query problems, it does not provide the optimal solution. RRT* [10], an extension to RRT, provides an asymptotically optimal solution, i.e., RRT* invariably converges to an associated best or optimal solution if adequate run time is provided. ...
Sampling-based path planning algorithms are popularly used in autonomous mobile robot navigation applications. Optimal Rapidly exploring Random Trees (RRT*) is one of the well-known sampling-based single-query path planning algorithms and it is asymptotically optimal, but its convergence is slow. To address the slow convergence problem of the RRT* algorithm, this paper proposes a directional RRT* algorithm called D-RRT*. The key idea of D-RRT* is to reduce the sampling space. This is achieved in this proposed work by focusing on the direction of the goal from the starting configuration through a simple elliptical heuristic formed between them. The proposed methodology is validated in two different cluttered 2D environments and compared with existing algorithms. The proposed D-RRT* path planning algorithm outperforms the RRT* in three performance measures: the initial cost solution, convergence time, and the number of nodes visited. The convergence rate of the proposed D-RRT* is improved over RRT* by 8.5% and 14.7% in the two cluttered environments considered. Also, the proposed D-RRT* algorithm is validated in a real-time environment using the TurtleBot3 robot.
Path planning algorithms determine the performance of the ambient intelligence navigation schemes in autonomous mobile robots. Sampling-based path planning algorithms are widely employed in autonomous mobile robot applications. RRT*, or Optimal Rapidly Exploring Random Trees, is a very effective sampling-based path planning algorithm. However, the RRT* solution converges slowly. This study proposes a directional random sampling-based RRT* path planning algorithm known as DR-RRT* to address the slow convergence issue. The novelty of the proposed method is that it reduces the search space by combining directional non-uniform sampling with uniform sampling. It employs a random selection approach to combine the non-uniform directional sampling method with uniform sampling. The proposed path planning algorithm is validated in three different environments with a map size of 384*384, and its performance is compared to two existing algorithms: RRT* and Informed RRT*. Validation is carried out utilizing a TurtleBot3 robot with the Gazebo Simulator and the Robotics Operating System (ROS) Melodic. The proposed DR-RRT* path planning algorithm is better than both RRT* and Informed RRT* in four performance measures: the number of nodes visited, the length of the path, the amount of time it takes, and the rate at which the path converges. The proposed DR-RRT* global path planning algorithm achieves a success rate of 100% in all three environments, and it is suited for use in all kinds of environments.
As one of the commonly used vehicles for underwater detection, underwater robots are facing a series of problems. The real underwater environment is large-scale, complex, real-time and dynamic, and many unknown obstacles may exist in the underwater environment. Under such complex conditions and lack of prior knowledge, the existing path planning methods are difficult to plan, therefore they cannot effectively meet the actual demands. In response to these problems, a three-dimensional marine environment including multiple obstacles is established with the real ocean current data in this paper, which is consistent with the actual application scenarios. Then, we propose an N-step Priority Double DQN (NPDDQN) path planning algorithm, which potently realizes obstacle avoidance in the complex environment. In addition, this study proposes an experience screening mechanism, which screens the explored positive experience and improves its reuse rate, thus efficiently improving the algorithm stability in the dynamic environment. This paper verifies the better performance of reinforcement learning compared with a variety of traditional methods in three-dimensional underwater path planning. Underwater robots based on the proposed method have good autonomy and stability, which provides a new method for path planning of underwater robots.
Note to Practitioners
—The goal of this study is to provide a new solution for obstacle avoidance in path planning of underwater robots, which is consistent with the dynamic and real-time demands of the real environment. Existing underwater path planning researches lack a consistent environment with the actual application, and therefore we firstly construct a three-dimensional ocean environment with real ocean current data to provide support for the algorithms. Additionally, most of the algorithms are pre-planning methods or require long-time calculation, and there is little research on obstacle avoidance. In the face of obstacle changes, underwater robots with poor adaptability will cause performance decline and even economic losses. The proposed algorithm learns through interaction with the environment, and therefore it does not require any prior experience, and has good adaptability as well as fast inference speed. Especially, in the dynamic environment, algorithm performance is difficult to guarantee due to less positive experience in exploration. The proposed experience screening mechanism improves the stability of the algorithm, so that the underwater robot maintains stable performance in different dynamic environments.
This paper reviews the literature on the path planning of mobile robots using Robot Operating System (ROS). Three different types of path planning algorithms are considered here. These are the Generalized Voronoi Diagrams (GVD), a Rapidly Exploring Random Tree (RRT), and the Gradient Descent Algorithm (GDA). The importance of each algorithm with its advantages and disadvantages is discussed here. It is highlighted that GDA is a better candidate for single query problems as its generation time is shorter than RRT and its path length is optimal as the use of Voronoi Diagrams is the preferred choice for multi-query planning. A total of 33 papers were surveyed in this research area, covering contributions on each algorithm for mobile robot path planning in the 24-year timeframe of 1998-2021.
Open-ended human environments, such as pedes-trian streets, hospital corridors, train stations etc., are places where robots start to emerge. Hence, being able to plan safe and natural trajectories in these dynamic environments is an important skill for future generations of robots. In this work the problem is formulated as planning a minimal cost trajectory through a potential field, defined from the perceived position and motion of persons in the environment. A modified Rapidly-exploring Random Tree (RRT) algorithm is proposed as a solution to the planning problem. The algorithm implements a new method for selecting the best trajectory in the RRT, according to the cost of traversing a potential field. Furthermore the RRT expansion is enhanced to direct the search and account for the kinodynamic robot constraints. A model predictive control (MPC) approach is taken to accommodate for the uncertainty in the dynamic environment. The planning algorithm is demonstrated in a simulated pedes-trian street environment.
Humanoid robotics hardware and control techniques have advanced rapidly during the last five years. Presently, several companies have announced the commercial availability of various humanoid robot prototypes. In order to improve the autonomy and overall functionality of these robots, reliable sensors, safety mechanisms, and general integrated software tools and techniques are needed. We believe that the development of practical motion planning algorithms and obstacle avoidance software for humanoid robots represents an important enabling technology. This paper gives an overview of some of our recent efforts to develop motion planning methods for humanoid robots for application tasks involving navigation, object grasping and manipulation, footstep placement, and dynamically-stable full-body motions. We show experimental results obtained by implementations running within a simulation environment as well as on actual humanoid robot hardware.
Rapidly-exploring random trees (RRTs) are widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swing up task, and on path planning for a nonholonomic car.
This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot's environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot's high-dimensional configuration space. Kinodynamic planning is treated as a motion-planning problem in a higher dimensional state space that has both first-order differential constraints and obstacle based global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized path-planning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized planning approach that is particularly tailored to trajectory planni ng problems in high-dimensional state spaces. The basis for this approach is the construction of rapidly exploring random trees, which offer benefits that are similar to those obtained by successful randomized holonomic planning methods but apply to a much broader class of problems. Theoretical analysis of the algorithm is given. Experimental results are presented for an implementation that computes trajectories for hovercrafts and satellites in cluttered environments, resulting in state spaces of up to 12 dimensions.
Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. Written for computer scientists and engineers with interests in artificial intelligence, robotics, or control theory, this is the only book on this topic that tightly integrates a vast body of literature from several fields into a coherent source for teaching and reference in a wide variety of applications. Difficult mathematical material is explained through hundreds of examples and illustrations.
We present a sampling-based path planning and replanning algorithm that produces anytime solutions. Our algorithm tunes the quality of its result based on available search time by generating a series of solutions, each guaranteed to be better than the previous ones by a user-defined improvement bound. When updated information regarding the underlying search space is received, the algorithm efficiently repairs its previous solution. The result is an approach that provides low-cost solutions to high-dimensional search problems involving partially-known or dynamic environments. We discuss theoretical properties of the algorithm, provide experimental results on a simulated multirobot planning scenario, and present an implementation on a team of outdoor mobile robots
The range searching problem is a fundamental problem in computational geometry, with numerous important applications. Most research has focused on solving this problem exactly, but lower bounds show that if linear space is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges. In this paper we show that if one is willing to allow approximate ranges, then it is possible to do much better. In particular, given a bounded range Q of diameter w and ε>0, an approximate range query treats the range as a fuzzy object, meaning that points lying within distance εw of the boundary of Q either may or may not be counted. We show that in any fixed dimension d, a set of n points in can be preprocessed in time and space, such that approximate queries can be answered in time. The only assumption we make about ranges is that the intersection of a range and a d-dimensional cube can be answered in constant time (depending on dimension). For convex ranges, we tighten this to time. We also present a lower bound for approximate range searching based on partition trees of , which implies optimality for convex ranges (assuming fixed dimensions). Finally, we give empirical evidence showing that allowing small relative errors can significantly improve query execution times.